In the design of singlet optical lenses for certain applications in the optical spectrum at wide angles off-axis it is sometimes desired to achieve greater off-axis angles of operation in one plane than in the other, greater azimuth performance usually being sought in preference to better elevation performance. Due to requirements for weight minimization and compact packaging for aircraft and space craft vehicle installations where both system volume and weight are at a premium, it is further sometimes desirable to extremize the lens in the sense of maximizing the lens aperture or minimizing the lens volume and sometimes simultaneously to achive a minimum, or at any rate a near minimum, F-number.
On the other hand, using modern nonspherical lens fabrication and grinding techniques there is no need to restrict the lens design to spherical surfaces grindable only by self-correcting motions as in classical optical lens manufacture, but rather, nonspherical lenses of quite complex shape may be readily used. With this relaxation of the design requirements, consideration was first given to nonspherical but rotationally invariant lenses, i.e., nonspherical lenses whose surfaces are surfaces of revolution about the lens axis such as the aplanatic, and generalized aplanatic lenses of L. C. Martin, and R. L. Sternberg. Such lenses, however, like any ordinary singlet lens, spherical or nonspherical, invariably suffer when extremized from astigmatism at off-axis points with the magnitude of that aberration increasing with increasing angles off-axis and decreasing F-number.